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Hollywood star Matt Damon has backed a woman to take over from him in the box-office hit Bourne franchise.

Speaking at the European Premiere of the fifth instalment Jason Bourne, the actor said: “It’s going to happen at some point. An actress, a girl could do it. I think there are a lot of interesting ways they could go with it.”

His comments follow similar calls for a woman to play the newest Bond, with the front-runners all men. James Norton is the current bookie's favourite to be the next 007. The X-Files actor Gillian Anderson notoriously threw her name in to the ring on Twitter in May, claiming “It’s Bond. Jane Bond.”

Damon, 45, previously ruled himself out of ever playing the British spy, saying that “he’s a misogynist, he swills martinis and kills people and cracks jokes about it” and that his Bourne has “today’s values; Bond has the values of the 1960s.”

Jason Bourne is Damon’s fourth outing as the title character in the five-film strong franchise, so there’s more than enough potential for a woman to take over the lead role in the near future. He spoke of his future within the franchise, saying “they make it as easy as they can for me. The older you get the harder it gets.”

Matt attended the European premiere of Jason Bourner with his wife Luciana Barroso (Photo: FameFlynet)

Luciana turned heads in a thigh high pink dress (Photo: WireImage)

With its European Premiere taking place in London's Leicester Square, the latest instalment in the £927million block-buster franchise, follows on from Bourne’s disappearance at the end of The Bourne Ultimatum. The former CIA agent travels through London, Las Vegas and Greece to find answers about his past in a fast-paced series of car chases and high-throttle scenes.

Julia Stiles returns to the series as Bourne’s ally Nicky Morgan, describing Nicky as “a lot more rebellious. She’s turned against the CIA and has a lot of information she wants to expose.” Before she heads up the upcoming Tomb Raider reboot, Oscar-winning actress Alicia Vikander is the new-comer to the franchise as Heather Lee, a CIA agent who finds herself intertwined with Bourne's world.

Matt Damon last hit our screens as Bourne in 2007, stating at the time that he would not be in another film if director Paul Greengrass was not on board. Jason Bourne follows on from The Bourne Legacy, staring Jeremy Renner, which paid homage to Damon’s character but did not feature him as the main protagonist.

Jeremy Renner took over the lead role for one movie before Matt stepped back into the part (Photo: Rex)

Damon also continued his long-standing objection to Presidential candidate Donald Trump, saying “I can think of about a hundred million people who I would rather do it than him.” This follows Damon previously branding Trump as “petty” and “thin-skinned”.